31 Aug 2001
I suppose I should close out this month, a little too jam-packed of activity for
an August (remember, I spent my first 7 years in Savannah, where one can =die=
if one is a little too active in August), with a calming remark or two.
January is not the month of endings and beginnings -- August is.
One of the things I'm doing today (recovering from a burnt finger, and it still
bites like a bear when I get my pinky anywhere near something hot (like tea)) is
searching for mathematical poetry in my very small poetry collection (and in
some varied math books, which I have a good suspicion contain poetry (like
Godel, Escher, Bach)). Some I knew I would find before looking: "Euclid Alone
Has Looked on Beauty Bare" by Edna St. Vincent Millay and "A Valediction:
Forbidding Mourning" by John Donne. I heartily disagree with Millay, but she
reflects what many poets looking from the outside see - the beauty in geometry,
the patterns and the forms which are the essence at the heart of mathematics. I
found a poem by Wordsworth reflecting this perceived perfection, while decrying
that he can do little of it himself.
These things make me sad.
I know the mathematicians who read this will knowingly nod their heads (except
for the bastards who like to use mathematics as their Litmus test for People Who
Count (=cough=). There are those who think that their eminent grasp of Category
Theory and Differential Geometry make them better than the hoi polloi who don't
even know these things exist.) How often, when at a party, a gathering, of
family or strangers, when finding out one is a mathematician will say something
on the order of "I never was very good at math." or "I always hated math." There
are worse things that have been said, but there's no reason to bring up bad
memories -- those statements shall suffice. Consider, had I responded to a
person with "Oh, I always hated reading." or "I never understood history." Would
you respect me as an educated person? People can go around, claiming never to
understand percentages, proofs, or postulates, and have their credentials as a
high-level intellectual.
Some of this has been reflected in the standard requirements at colleges: those
in the physical and mathematical sciences are forced to take high-level courses
in literature, history, and foreign language. I had to take classes that were
taken by juniors majoring in english. However, those in the humanities are
required to take the barest of science and math classes - usually nothing beyond
the freshman level, though sometimes a sophomore level. Never something that
junior majors attend.
This is wrong.
At my high school, the North Carolina School of Science and Math, we were
required to take a math class every semester, an English class every semester, 3
years of Science classes (1 of biology, chemistry, and physics each -- so on
average 1.5 science classes per semester), 1 year worth of social studies. I'm
sure we may have been required to do some other things as well - oh yeah, a sum
total of two years of a foreign language (if one took the first year at the
"home school" (NCSSM was only junior and senior years) you needed to take only
one). I knew people who went to NCSSM solely due to the excellence of the art
studio (we started a stained glass window for our western-exposure windows; the
studio used to be the surgery room of Watts Hospital, its buildings being the
original home of S&M, and further expanded over the years - since the hospital
was built in 1908, most light was from ambient sources), but these people had to
fulfill the math and science requirements, which were rather rigorous. All the
teachers at NCSSM have at least a masters degree, usually in the subject matter
they teach; many have doctorates. Most have taught on the college level. That's
not to say we took undergraduate-level classes; many of the classes were much
harder. They were definitely more work intensive. I remember my junior English
teacher telling us, "I had to teach the five-paragraph essay at UNC-Chapel Hill.
You are smarter than Carolina freshmen. You will not submit a formula essay to
me unless you want an F."
The science and math courses I took: CalcBC, Calc III, Fractals & Chaos, Number
Theory, Math Modelling, Math Self-Study (ok, that one was a joke), AP Chemistry,
Genetics, Cell Bio, Polymer Chemistry, Physics (with Topics), AP Physics, Modern
Physics, Astrophysics, Electronics
I think that covers it all.
Non-S/M courses I took: General Art (drawing, photography, silkscreening and
printmaking, other stuff which I don't remember), Electronic Music, American
Literature, WRRD (Wisdom, Reason, Revelation, and Doubt -- Western Lit &
History), French 2
And for Special Projects Week, both years I picked Art projects.
And remember, those are the official classes I took, in my last two years in
high school.
In college, non-S/M classes I took: Math, Music, and Models, Computer Music
Composition, History of Ancient and Medieval Science, Science Fiction, Freshman
Comp, 3 years of Japanese, 2 years of P.E., Sociolinguistics
That's all I can remember off the top of my head.
Totally separate of my "official" education, I go to art museums, art music
concerts (modern and classical), read great works of literature, attend plays,
dance pieces, musicals... etc. I would say I'm a pretty well-rounded person,
and most of the people I know in math have many non-science and math interests.
What is sad is that many who specialize in the humanities have no science or
math interests, or feel that a surface acknowledgement of these fields passes
for a well-rounded mindview.
I was entirely taken aback when I had to show my guitar teacher the Pythagorean
Theorem, very possibly the best-known theorem (I don't count Fermat's Last
Theorem, because people don't really =know= it, they just know =of= it. Besides,
FLT is based on a reaction to the PT), when I was showing him how to make
certain geometric constructions so he could try out new guitar designs. I was
disgusted when I heard from my freshman Calc I students that they didn't know
the formula for the area of a circle. Had I said "Shakespeare who?" in my
Freshman comp class, I would be put down as an utter illiterate. But since
people like to think of math and science as necklaces of facts, in which each
bead is separate, they feel it's understandable if one has lost a few; I could
note in this metaphor that when one loses one bead off of a necklace, generally
the ones behind it fall off as well.
My particular tirades about infinity were an attempt to show different areas of
mathematics in which infinity rears its incomprehensible head. It's useful for
mathematicians even to step back for a moment and remember where their little
corner of the world hooks up to everything else. A long time ago, about 200
years ago, mathematics had only two real divisions: geometry and everything
else; still, at that time, all of the sciences and maths were pulled together
into a whole called Natural Philosophy. I wish we went back to that model; I
myself have to think about research from neuroscience all the time, to consider
what is reasonable from a physical point of view, just as I am considering the
mathematical possibilities of the numerical techniques I am using. I love
probability, and I often have in mind many of its outcroppings into statistics
and actuarial tables and even its origins in gambling (most particularly, dice
gambling). I think of probability when I hear the latest reports on risk
factors for heart disease; I think of probability when I run into a friend at
the Met Museum of Art at random; I play with probability when I try my luck at
backgammon or poker; I wrestle with probability when I consider the movement of
financial markets; I immerse myself in probability when I consider the quantum
clouds that make up this being I like to call Mary Pat Campbell(and which others
like to call Meep ("Some call me....Tim.")).
I do not solely bring my math with me when I look at the world, I have my webs
from my reading of Dickens, Donne, and Dawkins, I have my mystic view informed
by my studies in Catholicism and Physics, I have my experiences of looking at
great works by Rodin, Dali, or Van Gogh, I have my internal soundtrack supplied
by Chopin, Dvorak, Bach, and Cage. I keep extending my world, trying to reach
out with my senses - supplementing my touch with knitting and braille,
tantalizing my smell and taste with baking and shopping at the greenmarket,
bombarding my brain with the ambient sounds of NYC, resting my eyes on the
complex interplay of architecture of the city and its incidental greenery.
To those who have reacted to math and science with fear or hate, and I do not
blame you when one is so often taught in one's younger years by people who also
fear and hate math (and then run into S/M profs who telegraph their disdain for
those who don't follow their opaque terminology), I want you to realize you are
now blind to entire dimensions of reality. People say that math and science
soullessly dissect the world, that there is no beauty in our flat truths. By
buying into this proposition, you are willingly allowing yourself to remain
chained in Plato's cave - you see the shadows on the wall, but you do not see
the solid objects casting the shadows, for you cannot move your head to look in
a different direction. Imagine that you were even more restricted - that you
could not read . The thoughts and ideas available to you would be restricted to
that of what those near you say, or what is on the T.V. or radio. The vast
resources of the web would be closed to you. Almost all poetry would be closed
to you (except for the poetry that makes itself into popular song (and there is
some, just check out Sting)). Your horizon would be so close, the journey to it
would almost be worthless. Having the worlds of math and science closed to you
is no different.
But how to break into this forbidding subject?
Just as I am soon to embark into joining a group which tapes educational texts
for those who can't read (I hope to specialize in math and science books), and
as one day I hope to transcribe important math books into Braille, there are
plenty of people out there who have written books, recorded lectures, made web
sites for those to whom these things are forbidding.
I will name a few places which I think are useful: The Teaching Company
(www.teachco.com), which has excellent lectures on Science and Math - I
recommend "The Joy of Mathematics" with Murray Siegel. He touches on great
swaths of math. I have it around the apt. somewhere (I got it for Stuart). I've
bought their lectures on Neurophysiology and Anatomy. The Anatomy tapes are
great (though a little scary to find out everything that can go wrong.) If
you're a hard sciences person who hasn't really explored history or literature,
they have stuff for you, too. I have all their lectures on Shakespeare, series
on Chaucer and Milton, stuff on the history of the English language.
There are many popularizers out there: Martin Gardner has many books of math
columns, though I will tell you much of it is "light", recreational math (though
much of it is related to "deeper" math). I personally adore Douglas
Hofstadter's Godel, Escher, Bach, but I don't recommend it to a newcomer to
math, as some of it can be particularly daunting and it really does require some
hard thinking. Stephen Jay Gould, Carl Sagan, and Isaac Asimov have all written
excellent popular science books; some of the books are collections of essays,
some treat a particular slice of science (like Gould's =The Mismeasure of Man=).
I could say that you should go to the Science section at Barnes & Noble, but
there's quite a bit of crap out there as well, though I think it's more
difficult to get a crappy science book published than a crappy fiction book.
I'm thinking of making a links page for this stuff, but I probably won't. Y'all
have to do =some= work on your own, or you might value the knowledge as cheap.
Too often one has the attitude "You get what you pay for" (I often say this, but
usually as a bald attempt to coerce people into giving me money.)
Still, as someone once said "Truth is One". The problem is we are limited as
humans, but we can see this Truth better if we have more ways of looking at it.
So get yourself some more points of view.